# A Canonical Dynamic Macroeconomic General Equilibrium Model in Timeline Form (see Torres, 2016) A canonical dynamic macroeconomic general equilibrium model in timeline form (see Torres, 2016, Table 2.1 and 2.2). The firm has a CESAK production function. ```r gemCanonicalDynamicMacroeconomic_Timeline_2_2( alpha.firm = rep(1, 4), es.prod.lab.firm = 1, beta.prod.firm = 0.35, depreciation.rate = 0.06, eis = 1, Gamma.beta = 0.97, beta.prod.consumer = 0.4, es.prod.lab.consumer = 1, gr = 0, initial.product.supply = 200, head.tail.adjustment = "both", wage.payment = "post", beta.consumer = NULL, ... ) ``` ## Arguments - `alpha.firm`: a positive vector, indicating the efficiency parameters of the firm for each economic period. The number of economic periods will be set to length(alpha.firm) + 1. - `es.prod.lab.firm`: the elasticity of substitution between product and labor in the production function of the firm. - `beta.prod.firm`: the share parameter of the product in the production function. - `depreciation.rate`: the physical depreciation rate of capital stock. - `eis`: a positive scalar indicating the elasticity of intertemporal substitution of the consumer. - `Gamma.beta`: the subjective discount factor of the consumer. - `beta.prod.consumer`: the share parameter of the product in the period utility function. - `es.prod.lab.consumer`: the elasticity of substitution between product and labor in the CES-type period utility function of the consumer. - `gr`: the growth rate of the labor supply. - `initial.product.supply`: the initial product supply. - `head.tail.adjustment`: a character string specifying the type of the head-tail-adjustment policy, must be one of "both" (default), "head", "tail" or "none". - `wage.payment`: a character string specifying the wage payment method, must be one of "pre" or "post". - `beta.consumer`: NULL (the default) or a positive vector containing length(alpha.firm) + 1 elements specifying the consumer's intertemporal share parameter. If beta.consumer is not NULL, Gamma.beta will be ignored. - `...`: arguments to be passed to the function sdm2. ## Examples ```r #### Take the wage postpayment assumption. ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2() np <- 5 eis <- 1 Gamma.beta <- 0.97 gr <- 0 ge$p ge$p[1:(np - 1)] / ge$p[2:np] - 1 ge$p[(np + 1):(2 * np - 2)] / ge$p[(np + 2):(2 * np - 1)] - 1 sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr) # the steady-state equilibrium return rate ge$z ge$D node_plot(ge$dst.consumer, TRUE) #### Take the wage postpayment assumption. eis <- 0.8 Gamma.beta <- 0.97 gr <- 0.03 ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2( es.prod.lab.firm = 0.8, eis = eis, Gamma.beta = Gamma.beta, es.prod.lab.consumer = 0.8, gr = gr ) np <- 5 ge$p growth_rate(ge$p[1:np]) 1 / (1 + sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr)) - 1 ge$z growth_rate(ge$z[1:(np - 1)]) ge$D ge$S ##### a fully anticipated technology shock. ## Warning: Running the program below takes several minutes. # np <- 120 # alpha.firm <- rep(1, np - 1) # alpha.firm[40] <- 1.05 # ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(alpha.firm = alpha.firm) # ## The steady state product supply is 343.92. ## the (economic) time series of product supply. # plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20) ## The steady state product consumption is 57.27. ## the (economic) time series of product consumption. # plot(ge$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20) # plot(growth_rate(ge$p[1:(np)]), type = "o", pch = 20) # plot(growth_rate(ge$p[(np + 1):(2 * np)]), type = "o", pch = 20) # ##### an unanticipated technology shock. # np <- 50 # alpha.firm <- rep(1, np - 1) # alpha.firm[1] <- 1.05 # ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2( # alpha.firm = alpha.firm, # initial.product.supply = 286.6341, # the steady state value # head.tail.adjustment = "tail" # ) # ## The steady state product supply is 343.92. ## the (economic) time series of product supply. # plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20) ## The steady state product consumption is 57.27. ## the (economic) time series of product consumption. # plot(ge$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20) # plot(growth_rate(ge$p[1:(np)]), type = "o", pch = 20) # plot(growth_rate(ge$p[(np + 1):(2 * np)]), type = "o", pch = 20) # ### a technology shock anticipated several periods in advance. # np <- 50 # alpha.firm <- rep(1, np - 1) # alpha.firm[5] <- 1.05 # ge5 <- gemCanonicalDynamicMacroeconomic_Timeline_2_2( # alpha.firm = alpha.firm, # initial.product.supply = 286.6341, # the steady state value # head.tail.adjustment = "tail" # ) # ## The steady state product supply is 343.92. ## the (economic) time series of product supply # plot(ge5$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20) ## The steady state product consumption is 57.27. ## the (economic) time series of product consumption # plot(ge5$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20) # plot(growth_rate(ge5$p[1:(np)]), type = "o", pch = 20) # plot(growth_rate(ge5$p[(np + 1):(2 * np)]), type = "o", pch = 20) # # alpha.firm <- rep(1, np - 1) # alpha.firm[10] <- 1.05 # ge10 <- gemCanonicalDynamicMacroeconomic_Timeline_2_2( # alpha.firm = alpha.firm, # initial.product.supply = 286.6341, # the steady state value # head.tail.adjustment = "tail" # ) # plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20, ylim = c(-0.005, 0.017)) # lines(ge5$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 21) # lines(ge10$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 22) ##### an unanticipated technology shock. ## Warning: Running the program below takes several minutes. # np <- 100 # alpha.firm <- exp(0.01) # for (t in 2:(np - 1)) { # alpha.firm[t] <- exp(0.9 * log(alpha.firm[t - 1])) # } # plot(alpha.firm) # # ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2( # alpha.firm = alpha.firm, # initial.product.supply = 286.6341, # the steady state value # head.tail.adjustment = "tail" # ) # ## The steady state product supply is 343.92. ## the (economic) time series of product supply # plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20) ## The steady state product consumption is 57.27. ## the (economic) time series of product consumption # plot(ge$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20) # plot(growth_rate(ge$p[1:(np)]), type = "o", pch = 20) # plot(growth_rate(ge$p[(np + 1):(2 * np)]), type = "o", pch = 20) #### Take the wage prepayment assumption. ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(wage.payment = "pre") np <- 5 eis <- 1 Gamma.beta <- 0.97 gr <- 0 ge$p ge$p[1:(np - 1)] / ge$p[2:np] - 1 ge$p[(np + 1):(2 * np - 2)] / ge$p[(np + 2):(2 * np - 1)] - 1 sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr) # the steady-state equilibrium return rate ge$z ge$D node_plot(ge$dst.consumer, TRUE) #### Take the wage prepayment assumption. np <- 5 eis <- 0.8 Gamma.beta <- 0.97 gr <- 0.03 ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2( es.prod.lab.firm = 0.8, eis = eis, Gamma.beta = Gamma.beta, es.prod.lab.consumer = 0.8, gr = gr, wage.payment = "pre" ) ge$p growth_rate(ge$p[1:np]) 1 / (1 + sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr)) - 1 ge$z growth_rate(ge$z[1:(np - 1)]) ge$D ge$S ``` ## References Torres, Jose L. (2016, ISBN: 9781622730452) Introduction to Dynamic Macroeconomic General Equilibrium Models (Second Edition). Vernon Press. ## See Also `gemCanonicalDynamicMacroeconomic_TimeCircle_2_2`, `gemDynamicMacroeconomic_SpotTrading_3_2`, `gemCanonicalDynamicMacroeconomic_Sequential_WagePostpayment_4_3`.

gemCanonicalDynamicMacroeconomic_Timeline_2_2 function